Nick,
PBF is a system that was custom-designed for managing the budgeting process in public sector. It not only includes the BW-based Integrated Planning (BW-IP) engine but also Personnel Expenditure Planning - complete personnel cost projection tool which uses position and employee data to project payroll costs by fund, fund center, etc. It uses a Visual Composer user interface to create budget entry forms with ability to provide extensive detailed text, field-validation logic and an approval workflow. Reporting of budget requests is provided through BW reporting tools. A fair amount of the set up can be performed by a functional consultant with training.
As mentioned earlier BW-IP is the planning engine underlying PBF. Without the PBF application, you can create planning layouts (spreadsheet-like screens), planning formulas (copy, adjust by %, etc.) and a rudimentary stage notification process. Implementation always requires a BW-IP developer. BW-IP does not have extensive text-handling so it is difficult to maintain budget narratives using this tool.
BPC is a separate planning engine that SAP acquired through its acquisition of OutlookSoft. It has been ported from its origins in Microsoft products to a NetWeaver platform and can do all that BW-IP can do. As you noted, it will eventually replace BW-IP.
Thanks
Shyam